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Locally correcting polynomial codes Main idea: – Restricting a low-degree multivariate polynomial to a line gives a low- degree univariate polynomial So: – The value of P(a,b) can be recovered from the values of P on any line L through (a,b) – Even if there are errors Picking the line L at random Less than ± /2 errors on the line (univariate polynomial decoding) Decoding queries: – # points on a line = q ¼ k 0.5 Fq2Fq2 (a,b) L